Distinguishing attosecond electron-electron scattering and screening in transition metals

Method and computer library for calculation of the Boltzmann collision integrals on discrete momentum lattice

We present a general and numerically efficient method for calculation of collision integrals for interacting quantum gases on a discrete momentum lattice. Here we employ the original analytical approach based on Fourier transform covering a wide spectrum of solid-state problems with various particle statistics and arbitrary interaction models, including the case of momentum-dependent interaction. The comprehensive set of the transformation principles is given in detail and realized as a computer Fortran 90 library FLBE (Fast Library for Boltzmann Equation).

A beamline for ultrafast extreme ultraviolet magneto-optical spectroscopy in reflection near the shot noise limit

High harmonic generation (HHG) makes it possible to measure spin and charge dynamics in materials on femtosecond to attosecond timescales. However, the extreme nonlinear nature of the high harmonic process means that intensity fluctuations can limit measurement sensitivity. Here we present a noise-canceled, tabletop high harmonic beamline for time-resolved reflection mode spectroscopy of magnetic materials. We use a reference spectrometer to independently normalize the intensity fluctuations of each harmonic order and eliminate long term drift, allowing us to make spectroscopic measurements near the shot noise limit. These improvements allow us to significantly reduce the integration time required for high signal-to-noise (SNR) measurements of element-specific spin dynamics. Looking forward, improvements in the HHG flux, optical coatings, and grating design can further reduce the acquisition time for high SNR measurements by 1-2 orders of magnitude, enabling dramatically improved sensitivity to spin, charge, and phonon dynamics in magnetic materials.

Liquid-cooled modular gas cell system for high-order harmonic generation using high average power laser systems

We present the design and implementation of a new, modular gas target suitable for high-order harmonic generation using high average power lasers. To ensure thermal stability in this high heat load environment, we implement an appropriate liquid cooling system. The system can be used in multiple-cell configurations, allowing us to control the cell length and aperture size. The cell design was optimized with heat and flow simulations for thermal characteristics, vacuum compatibility, and generation medium properties. Finally, the cell system was experimentally validated by conducting high-order harmonic generation measurements using the 100 kHz high average power HR-1 laser system at the Extreme Light Infrastructure Attosecond Light Pulse Source (ELI ALPS) facility. Such a robust, versatile, and stackable gas cell arrangement can easily be adapted to different experimental geometries in both table-top laboratory systems and user-oriented facilities, such as ELI ALPS.

Attosecond spectroscopy for the investigation of ultrafast dynamics in atomic, molecular and solid-state physics

Since the first demonstration of the generation of attosecond pulses (1 as = 10^-18s) in the extreme-ultraviolet spectral region, several measurement techniques have been introduced, at the beginning for the temporal characterization of the pulses, and immediately after for the investigation of electronic and nuclear ultrafast dynamics in atoms, molecules and solids with unprecedented temporal resolution. The attosecond spectroscopic tools established in the last two decades, together with the development of sophisticated theoretical methods for the interpretation of the experimental outcomes, allowed to unravel and investigate physical processes never observed before, such as the delay in photoemission from atoms and solids, the motion of electrons in molecules after prompt ionization which precede any notable nuclear motion, the temporal evolution of the tunneling process in dielectrics, and many others. This review focused on applications of attosecond techniques to the investigation of ultrafast processes in atoms, molecules and solids. Thanks to the introduction and ongoing developments of new spectroscopic techniques, the attosecond science is rapidly moving towards the investigation, understanding and control of coupled electron-nuclear dynamics in increasingly complex systems, with ever more accurate and complete investigation techniques. Here we will review the most common techniques presenting the latest results in atoms, molecules and solids.

The 2021 ultrafast spectroscopic probes of condensed matter roadmap

In the 60 years since the invention of the laser, the scientific community has developed numerous fields of research based on these bright, coherent light sources, including the areas of imaging, spectroscopy, materials processing and communications. Ultrafast spectroscopy and imaging techniques are at the forefront of research into the light-matter interaction at the shortest times accessible to experiments, ranging from a few attoseconds to nanoseconds. Light pulses provide a crucial probe of the dynamical motion of charges, spins, and atoms on picosecond, femtosecond, and down to attosecond timescales, none of which are accessible even with the fastest electronic devices. Furthermore, strong light pulses can drive materials into unusual phases, with exotic properties. In this roadmap we describe the current state-of-the-art in experimental and theoretical studies of condensed matter using ultrafast probes. In each contribution, the authors also use their extensive knowledge to highlight challenges and predict future trends.

Attosecond intra-valence band dynamics and resonant-photoemission delays in W(110)

Time-resolved photoelectron spectroscopy with attosecond precision provides new insights into the photoelectric effect and gives information about the timing of photoemission from different electronic states within the electronic band structure of solids. Electron transport, scattering phenomena and electron-electron correlation effects can be observed on attosecond time scales by timing photoemission from valence band states against that from core states. However, accessing intraband effects was so far particularly challenging due to the simultaneous requirements on energy, momentum and time resolution. Here we report on an experiment utilizing intracavity generated attosecond pulse trains to meet these demands at high flux and high photon energies to measure intraband delays between sp- and d-band states in the valence band photoemission from tungsten and investigate final-state effects in resonant photoemission.

Accessing intraband dynamics is challenging due to simultaneous requirements on energy, momentum and time resolution. Here, the authors measure intraband delays between sp- and d-band electronic states in the valence band photoemission from W(110) using intracavity generated attosecond pulse trains.

Effect of transport current on suppression of superconductivity with ultrashort laser pulse

We study the suppression of superconductivity with ultrashort laser pulse in the presence of transport current. The theoretical model is based on the Bardeen-Cooper-Schrieffer relations for the superconducting state coupled with kinetic equations for nonequilibrium Bogoliubov quasiparticles and phonons. The results of numerical simulation for picosecond and femtosecond laser pulses of optical and infrared ranges are given. We discuss the effects of main problem parameters, including the current density.

Coherent Fourier scatterometry using orbital angular momentum beams for defect detection

Defect inspection on lithographic substrates, masks, reticles, and wafers is an important quality assurance process in semiconductor manufacturing. Coherent Fourier scatterometry (CFS) using laser beams with a Gaussian spatial profile is the standard workhorse routinely used as an in-line inspection tool to achieve high throughput. As the semiconductor industry advances toward shrinking critical dimensions in high volume manufacturing using extreme ultraviolet lithography, new techniques that enable high-sensitivity, high-throughput, and in-line inspection are critically needed. Here we introduce a set of novel defect inspection techniques based on bright-field CFS using coherent beams that carry orbital angular momentum (OAM). One of these techniques, the differential OAM CFS, is particularly unique because it does not rely on referencing to a pre-established database in the case of regularly patterned structures with reflection symmetry. The differential OAM CFS exploits OAM beams with opposite wavefront or phase helicity to provide contrast in the presence of detects. We numerically investigated the performance of these techniques on both amplitude and phase defects and demonstrated their superior advantages-up to an order of magnitude higher in signal-to-noise ratio-over the conventional Gaussian beam CFS. These new techniques will enable increased sensitivity and robustness for in-line nanoscale defect inspection and the concept could also benefit x-ray scattering and scatterometry in general.

Distinction of Electron Dispersion in Time-Resolved Photoemission Spectroscopy

While recent experiments provided compelling evidence for an intricate dependence of attosecond photoemission-time delays on the solid's electronic band structure, the extent to which electronic transport and dispersion in solids can be imaged in time-resolved photoelectron (PE) spectra remains poorly understood. Emphasizing the distinction between photoemission time delays measured with two-photon, two-color interferometric spectroscopy, and transport times, we demonstrate how the effect of energy dispersion in the solid on photoemission delays can, in principle, be observed in interferometric photoemission. We reveal analytically a scaling relation between the PE transport time in the solid and the observable photoemission delay and confirm this relation in numerical simulations for a model system. We trace photoemission delays to the phase difference the PE accumulates inside the solid and, in particular, predict negative photoemission delays. Based on these findings, we suggest a novel time-domain interferometric solid-state energy-momentum-dispersion imaging method.

Femtosecond X-ray induced changes of the electronic and magnetic response of solids from electron redistribution

Resonant X-ray absorption, where an X-ray photon excites a core electron into an unoccupied valence state, is an essential process in many standard X-ray spectroscopies. With increasing X-ray intensity, the X-ray absorption strength is expected to become nonlinear. Here, we report the onset of such a nonlinearity in the resonant X-ray absorption of magnetic Co/Pd multilayers near the Co L[Formula: see text] edge. The nonlinearity is directly observed through the change of the absorption spectrum, which is modified in less than 40 fs within 2 eV of its threshold. This is interpreted as a redistribution of valence electrons near the Fermi level. For our magnetic sample this also involves mixing of majority and minority spins, due to sample demagnetization. Our findings reveal that nonlinear X-ray responses of materials may already occur at relatively low intensities, where the macroscopic sample is not destroyed, providing insight into ultrafast charge and spin dynamics.

Attosecond Dynamics of sp-Band Photoexcitation

We report measurements of the temporal dynamics of the valence band photoemission from the magnesium (0001) surface across the resonance of the Γ[over ¯] surface state at 134 eV and link them to observations of high-resolution synchrotron photoemission and numerical calculations of the time-dependent Schrödinger equation using an effective single-electron model potential. We observe a decrease in the time delay between photoemission from delocalized valence states and the localized core orbitals on resonance. Our approach to rigorously link excitation energy-resolved conventional steady-state photoemission with attosecond streaking spectroscopy reveals the connection between energy-space properties of bound electronic states and the temporal dynamics of the fundamental electronic excitations underlying the photoelectric effect.

Revealing angular momentum transfer channels and timescales in the ultrafast demagnetization process of ferromagnetic semiconductors

Ultrafast control of magnetic order by light provides a promising realization for spintronic devices beyond Moore's Law and has stimulated intense research interest in recent years. Yet, despite 2 decades of debates, the key question of how the spin angular momentum flows on the femtosecond timescale remains open. The lack of direct first-principle methods and pictures for such process exacerbates the issue. Here, we unravel the laser-induced demagnetization mechanism of ferromagnetic semiconductor GaMnAs, using an efficient time-dependent density functional theory approach that enables the direct real-time snapshot of the demagnetization process. Our results show a clear spin-transfer trajectory from the localized Mn-d electrons to itinerant carriers within 20 fs, illustrating the dominant role of [Formula: see text] interaction. We find that the total spin of localized electrons and itinerant carriers is not conserved in the presence of spin-orbit coupling (SOC). Immediately after laser excitation, a growing percentage of spin-angular momentum is quickly transferred to the electron orbital via SOC in about 1 ps, then slowly to the lattice via electron-phonon coupling in a few picoseconds, responsible for the 2-stage process observed experimentally. The spin-relaxation time via SOC is about 300 fs for itinerant carriers and about 700 fs for Mn-d electrons. These results provide a quantum-mechanical microscopic picture for the long-standing questions regarding the channels and timescales of spin transfer, as well as the roles of different interactions underlying the GaMnAs demagnetization process.

Generation of extreme-ultraviolet beams with time-varying orbital angular momentum

Light fields carrying orbital angular momentum (OAM) provide powerful capabilities for applications in optical communications, microscopy, quantum optics, and microparticle manipulation. We introduce a property of light beams, manifested as a temporal OAM variation along a pulse: the self-torque of light. Although self-torque is found in diverse physical systems (i.e., electrodynamics and general relativity), it was not realized that light could possess such a property. We demonstrate that extreme-ultraviolet self-torqued beams arise in high-harmonic generation driven by time-delayed pulses with different OAM. We monitor the self-torque of extreme-ultraviolet beams through their azimuthal frequency chirp. This class of dynamic-OAM beams provides the ability for controlling magnetic, topological, and quantum excitations and for manipulating molecules and nanostructures on their natural time and length scales.

Role of initial magnetic disorder: A time-dependent ab initio study of ultrafast demagnetization mechanisms

Despite more than 20 years of development, the underlying physics of the laser-induced demagnetization process is still debated. We present a fast, real-time time-dependent density functional theory (rt-TDDFT) algorithm together with the phenomenological atomic Landau-Lifshitz-Gilbert model to investigate this problem. Our Hamiltonian considers noncollinear magnetic moment, spin-orbit coupling (SOC), electron-electron, electron-phonon, and electron-light interactions. The algorithm for time evolution achieves hundreds of times of speedup enabling calculation of large systems. Our simulations yield a demagnetization rate similar to experiments. We found that (i) the angular momentum flow from light to the system is not essential and the spin Zeeman effect is negligible. (ii) The phonon can play a role but is not essential. (iii) The initial spin disorder and the self-consistent update of the electron-electron interaction play dominant roles and enhance the demagnetization to the experimentally observed rate. The spin disorder connects the electronic structure theory with the phenomenological three-temperature model.

Recent advances in ultrafast X-ray sources

Over more than a century, X-rays have transformed our understanding of the fundamental structure of matter and have been an indispensable tool for chemistry, physics, biology, materials science and related fields. Recent advances in ultrafast X-ray sources operating in the femtosecond to attosecond regimes have opened an important new frontier in X-ray science. These advances now enable: (i) sensitive probing of structural dynamics in matter on the fundamental timescales of atomic motion, (ii) element-specific probing of electronic structure and charge dynamics on fundamental timescales of electronic motion, and (iii) powerful new approaches for unravelling the coupling between electronic and atomic structural dynamics that underpin the properties and function of matter. Most notable is the recent realization of X-ray free-electron lasers (XFELs) with numerous new XFEL facilities in operation or under development worldwide. Advances in XFELs are complemented by advances in synchrotron-based and table-top laser-plasma X-ray sources now operating in the femtosecond regime, and laser-based high-order harmonic XUV sources operating in the attosecond regime. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

High-flux ultrafast extreme-ultraviolet photoemission spectroscopy at 18.4 MHz pulse repetition rate

Laser-dressed photoelectron spectroscopy, employing extreme-ultraviolet attosecond pulses obtained by femtosecond-laser-driven high-order harmonic generation, grants access to atomic-scale electron dynamics. Limited by space charge effects determining the admissible number of photoelectrons ejected during each laser pulse, multidimensional (i.e. spatially or angle-resolved) attosecond photoelectron spectroscopy of solids and nanostructures requires high-photon-energy, broadband high harmonic sources operating at high repetition rates. Here, we present a high-conversion-efficiency, 18.4-MHz-repetition-rate cavity-enhanced high harmonic source emitting 5 × 105 photons per pulse in the 25-to-60-eV range, releasing 1 × 1010 photoelectrons per second from a 10-µm-diameter spot on tungsten, at space charge distortions of only a few tens of meV. Broadband, time-of-flight photoelectron detection with nearly 100% temporal duty cycle evidences a count rate improvement between two and three orders of magnitude over state-of-the-art attosecond photoelectron spectroscopy experiments under identical space charge conditions. The measurement time reduction and the photon energy scalability render this technology viable for next-generation, high-repetition-rate, multidimensional attosecond metrology.

Coherent light brightens the quantum science frontier

Controlling coherent light across a vast spectral range enables ultraprecise measurements and the quantum control of atomic, molecular, and condensed-matter systems.

Full-field imaging of thermal and acoustic dynamics in an individual nanostructure using tabletop high harmonic beams

Imaging charge, spin, and energy flow in materials is a current grand challenge that is relevant to a host of nanoenhanced systems, including thermoelectric, photovoltaic, electronic, and spin devices. Ultrafast coherent x-ray sources enable functional imaging on nanometer length and femtosecond timescales particularly when combined with advances in coherent imaging techniques. Here, we combine ptychographic coherent diffractive imaging with an extreme ultraviolet high harmonic light source to directly visualize the complex thermal and acoustic response of an individual nanoscale antenna after impulsive heating by a femtosecond laser. We directly image the deformations induced in both the nickel tapered nanoantenna and the silicon substrate and see the lowest-order generalized Lamb wave that is partially confined to a uniform nanoantenna. The resolution achieved-sub-100 nm transverse and 0.5-Å axial spatial resolution, combined with ≈10-fs temporal resolution-represents a significant advance in full-field dynamic imaging capabilities. The tapered nanoantenna is sufficiently complex that a full simulation of the dynamic response would require enormous computational power. We therefore use our data to benchmark approximate models and achieve excellent agreement between theory and experiment. In the future, this work will enable three-dimensional functional imaging of opaque materials and nanostructures that are sufficiently complex that their functional properties cannot be predicted.

Absolute timing of the photoelectric effect

Photoemission spectroscopy is central to understanding the inner workings of condensed matter, from simple metals and semiconductors to complex materials such as Mott insulators and superconductors¹. Most state-of-the-art knowledge about such solids stems from spectroscopic investigations, and use of subfemtosecond light pulses can provide a time-domain perspective. For example, attosecond (10^-18 seconds) metrology allows electron wave packet creation, transport and scattering to be followed on atomic length scales and on attosecond timescales^2-7. However, previous studies could not disclose the duration of these processes, because the arrival time of the photons was not known with attosecond precision. Here we show that this main source of ambiguity can be overcome by introducing the atomic chronoscope method, which references all measured timings to the moment of light-pulse arrival and therefore provides absolute timing of the processes under scrutiny. Our proof-of-principle experiment reveals that photoemission from the tungsten conduction band can proceed faster than previously anticipated. By contrast, the duration of electron emanation from core states is correctly described by semiclassical modelling. These findings highlight the necessity of treating the origin, initial excitation and transport of electrons in advanced modelling of the attosecond response of solids, and our absolute data provide a benchmark. Starting from a robustly characterized surface, we then extend attosecond spectroscopy towards isolating the emission properties of atomic adsorbates on surfaces and demonstrate that these act as photoemitters with instantaneous response. We also find that the tungsten core-electron timing remains unchanged by the adsorption of less than one monolayer of dielectric atoms, providing a starting point for the exploration of excitation and charge migration in technologically and biologically relevant adsorbate systems.

Imaging Plasmonic Fields with Atomic Spatiotemporal Resolution

We propose a scheme for the reconstruction of plasmonic near fields at isolated nanoparticles from infrared-streaked extreme-ultraviolet photoemission spectra. Based on quantum-mechanically modeled spectra, we demonstrate and analyze the accurate imaging of the IR-streaking-pulse-induced transient plasmonic fields at the surface of gold nanospheres and nanoshells with subfemtosecond temporal and subnanometer spatial resolution.

Colloidal crystal order and structure revealed by tabletop extreme ultraviolet scattering and coherent diffractive imaging

Colloidal crystals with specific electronic, optical, magnetic, vibrational properties, can be rationally designed by controlling fundamental parameters such as chemical composition, scale, periodicity and lattice symmetry. In particular, silica nanospheres -which assemble to form colloidal crystals- are ideal for this purpose, because of the ability to infiltrate their templates with semiconductors or metals. However characterization of these crystals is often limited to techniques such as grazing incidence small-angle scattering that provide only global structural information and also often require synchrotron sources. Here we demonstrate small-angle Bragg scattering from nanostructured materials using a tabletop-scale setup based on high-harmonic generation, to reveal important information about the local order of nanosphere grains, separated by grain boundaries and discontinuities. We also apply full-field quantitative ptychographic imaging to visualize the extended structure of a silica close-packed nanosphere multilayer, with thickness information encoded in the phase. These combined techniques allow us to simultaneously characterize the silica nanospheres size, their symmetry and distribution within single colloidal crystal grains, the local arrangement of nearest-neighbor grains, as well as to quantitatively determine the number of layers within the sample. Key to this advance is the good match between the high harmonic wavelength used (13.5nm) and the high transmission, high scattering efficiency, and low sample damage of the silica colloidal crystal at this wavelength. As a result, the relevant distances in the sample - namely, the interparticle distance (≈124nm) and the colloidal grains local arrangement (≈1μm) - can be investigated with Bragg coherent EUV scatterometry and ptychographic imaging within the same experiment simply by tuning the EUV spot size at the sample plane (5μm and 15μm respectively). In addition, the high spatial coherence of high harmonics light, combined with advances in imaging techniques, makes it possible to image near-periodic structures quantitatively and nondestructively, and enables the observation of the extended order of quasi-periodic colloidal crystals, with a spatial resolution better than 20nm. In the future, by harnessing the high time-resolution of tabletop high harmonics, this technique can be extended to dynamically image the three-dimensional electronic, magnetic, and transport properties of functional nanosystems.

Dynamical photo-induced electronic properties of molecular junctions

Nanoscale molecular-electronic devices and machines are emerging as promising functional elements, naturally flexible and efficient, for next-generation technologies. A deeper understanding of carrier dynamics in molecular junctions is expected to benefit many fields of nanoelectronics and power devices. We determine time-resolved charge current flowing at the donor-acceptor interface in molecular junctions connected to metallic electrodes by means of quantum transport simulations. The current is induced by the interaction of the donor with a Gaussian-shape femtosecond laser pulse. Effects of the molecular internal coupling, metal-molecule tunneling, and light-donor coupling on photocurrent are discussed. We then define the time-resolved local density of states which is proposed as an efficient tool to describe the absorbing molecule in contact with metallic electrodes. Non-equilibrium reorganization of hybridized molecular orbitals through the light-donor interaction gives rise to two phenomena: the dynamical Rabi shift and the appearance of Floquet-like states. Such insights into the dynamical photoelectronic structure of molecules are of strong interest for ultrafast spectroscopy and open avenues toward the possibility of analyzing and controlling the internal properties of quantum nanodevices with pump-push photocurrent spectroscopy.

Near- and Extended-Edge X-Ray-Absorption Fine-Structure Spectroscopy Using Ultrafast Coherent High-Order Harmonic Supercontinua

Recent advances in high-order harmonic generation have made it possible to use a tabletop-scale setup to produce spatially and temporally coherent beams of light with bandwidth spanning 12 octaves, from the ultraviolet up to x-ray photon energies >1.6  keV. Here we demonstrate the use of this light for x-ray-absorption spectroscopy at the K- and L-absorption edges of solids at photon energies near 1 keV. We also report x-ray-absorption spectroscopy in the water window spectral region (284-543 eV) using a high flux high-order harmonic generation x-ray supercontinuum with 10^{9}  photons/s in 1% bandwidth, 3 orders of magnitude larger than has previously been possible using tabletop sources. Since this x-ray radiation emerges as a single attosecond-to-femtosecond pulse with peak brightness exceeding 10^{26}  photons/s/mrad^{2}/mm^{2}/1% bandwidth, these novel coherent x-ray sources are ideal for probing the fastest molecular and materials processes on femtosecond-to-attosecond time scales and picometer length scales.

Critical behavior within 20 fs drives the out-of-equilibrium laser-induced magnetic phase transition in nickel

It has long been known that ferromagnets undergo a phase transition from ferromagnetic to paramagnetic at the Curie temperature, associated with critical phenomena such as a divergence in the heat capacity. A ferromagnet can also be transiently demagnetized by heating it with an ultrafast laser pulse. However, to date, the connection between out-of-equilibrium and equilibrium phase transitions, or how fast the out-of-equilibrium phase transitions can proceed, was not known. By combining time- and angle-resolved photoemission with time-resolved transverse magneto-optical Kerr spectroscopies, we show that the same critical behavior also governs the ultrafast magnetic phase transition in nickel. This is evidenced by several observations. First, we observe a divergence of the transient heat capacity of the electron spin system preceding material demagnetization. Second, when the electron temperature is transiently driven above the Curie temperature, we observe an extremely rapid change in the material response: The spin system absorbs sufficient energy within the first 20 fs to subsequently proceed through the phase transition, whereas demagnetization and the collapse of the exchange splitting occur on much longer, fluence-independent time scales of ~176 fs. Third, we find that the transient electron temperature alone dictates the magnetic response. Our results are important because they connect the out-of-equilibrium material behavior to the strongly coupled equilibrium behavior and uncover a new time scale in the process of ultrafast demagnetization.

Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin-orbit momentum conservation

Optical interactions are governed by both spin and angular momentum conservation laws, which serve as a tool for controlling light-matter interactions or elucidating electron dynamics and structure of complex systems. Here, we uncover a form of simultaneous spin and orbital angular momentum conservation and show, theoretically and experimentally, that this phenomenon allows for unprecedented control over the divergence and polarization of extreme-ultraviolet vortex beams. High harmonics with spin and orbital angular momenta are produced, opening a novel regime of angular momentum conservation that allows for manipulation of the polarization of attosecond pulses-from linear to circular-and for the generation of circularly polarized vortices with tailored orbital angular momentum, including harmonic vortices with the same topological charge as the driving laser beam. Our work paves the way to ultrafast studies of chiral systems using high-harmonic beams with designer spin and orbital angular momentum.